Dual-type strain wave gearing

ABSTRACT

An externally toothed gear of a dual-type strain wave gearing is provided with first and second external teeth having different teeth numbers. The first and second external teeth are flexed by a wave generator by the same flexing amount, into an ellipsoidal shape. The average pressure angle of main-tooth-surface sections of tooth profiles of the first external teeth having a low teeth number is less acute than the average pressure angle of main-tooth-surface sections of tooth profiles of the second external teeth having a high teeth number. Accordingly, a dual-type strain wave gearing can be achieved with which the first and second external teeth having different teeth numbers can be suitably flexed to form excellent meshing states with respective internally toothed gears.

TECHNICAL FIELD

The present invention relates to a strain wave gearing which has a pairof internally toothed gears, a cylindrical externally toothed gearcapable of flexing in a radial direction, and a wave generator.

BACKGROUND ART

Strain wave gearings having cylindrical externally toothed gears aretypically provided with a stationary-side internally toothed gearsecured so as not to rotate, a wave generator that is arotation-inputting element, a drive-side internally toothed gear that isa reduced-rotation-outputting element, and a cylindrical externallytoothed gear capable of flexing in the radial direction and meshing withthe stationary-side internally toothed gear and drive-side internallytoothed gear. In typical strain wave gearings, the externally toothedgear is caused to flex into an ellipsoidal shape, the ellipsoidallyflexed externally toothed gear meshing with the stationary-side anddrive-side internally toothed gears at both end positions along themajor axis of the ellipsoidal shape.

Patent Documents 1 and 4 disclose typical strain wave gearings in whichthe number of teeth of the stationary-side internally toothed gear istwo greater than that of the externally toothed gear, and the number ofteeth of the drive-side internally toothed gear is equal to that of theexternally toothed gear. In Patent Document 1, the external teeth of theexternally toothed gear are bisected at the tooth-trace-directioncentral portion thereof, one of the external-tooth portions beingcapable of meshing with the stationary-side internally toothed gear, andthe other of the external-tooth portions being capable of meshing withthe drive-side internally toothed gear. Patent Document 4 indicates thatthe rim wall thickness of the externally toothed gear dramaticallyaffects the tooth bottom fatigue strength of the externally toothedgear.

In the strain wave gearings disclosed in Patent Documents 1 and 5, whenthe wave generator rotates, the externally toothed gear rotates moreslowly at a speed ratio corresponding to the difference in the number ofteeth with respect to the stationary-side internally toothed gear. Thereduced rotation of the externally toothed gear is outputted from thedrive-side internally toothed gear, which rotates integrally with theexternally toothed gear.

Patent Document 2 discloses a strain wave gearing in which the number ofteeth of the stationary-side internally toothed gear is two greater thanthat of the externally toothed gear, and the number of teeth of thedrive-side internally toothed gear is two less than that of theexternally toothed gear. In this strain wave gearing, when the wavegenerator rotates, the externally toothed gear rotates more slowly at aspeed ratio corresponding to the difference in the number of teeth withrespect to the stationary-side internally toothed gear. The rotation ofthe externally toothed gear is increased at a speed ratio correspondingto the difference in number of teeth between the externally toothed gearand the drive-side internally toothed gear, and is outputted from thedrive-side internally toothed gear. The rotation outputted from thedrive-side internally toothed gear is reduced at a speed ratio of lessthan 50 in relation to the rotation inputted to the wave generator.

Patent Documents 2 and 3 disclose strain wave gearings having wavegenerators that have two rows of ball bearings. This type of wavegenerator is configured from a rigid plug having an ellipsoidallycontoured outer-peripheral surface, and two rows of ball bearings fittedto the outer-peripheral surface. The flexible externally toothed gear ispressed radially outward by the two major-axis end portions of theouter-peripheral surfaces of the ellipsoidally flexed outer races of theball bearings, and the meshing of the flexible externally toothed gearwith respect to the first and second rigid internally toothed gears issustained.

PRIOR ART DOCUMENTS Patent Documents

Patent Document 1: JP-A 2011-112214

Patent Document 2: JP-A 02-275147

Patent Document 3: JP-A 01-91151

Patent Document 4: 2008-180259

SUMMARY OF THE INVENTION Problems to be Solved by the Invention

It is considered that in the externally toothed gear used herein, firstteeth capable of meshing with one first internally toothed gear andsecond teeth capable of meshing with another second internally toothedgear are formed in the outer-peripheral surface of a radially flexiblecylindrical body, the second teeth differing in number from the firstteeth. Adopting such a configuration makes it possible to reduce orincrease the rotational speed between the first external teeth and afirst internally toothed gear, and to reduce or increase the rotationalspeed between the second external teeth and a second internally toothedgear, in a similar manner as in the strain wave gearing disclosed inPatent Document 2. Accordingly, it is possible to realize a strain wavegearing having a gear ratio of less than 50. Additionally, thisconfiguration enables a strain wave gearing having a speed ratio of lessthan 50 to be designed with a greater degree of freedom than in thestrain wave gearing disclosed in Patent Document 2.

In the present specification, a strain wave gearing that has anexternally toothed gear in which first and second external teethdiffering in number are formed in the outer-peripheral surface of aflexible cylindrical body is referred to as a “dual-type strain wavegearing.”

In a dual-type strain wave gearing, first external teeth and secondexternal teeth of an externally toothed gear are formed in theouter-peripheral surface of a shared cylindrical body, and the toothbottom rim parts of the first and second external teeth are connected toeach other. When the cylindrical body is caused by the wave generator toflex in an ellipsoidal shape, the first and second external teeth, whichdiffer in number, respectively mesh with separate internally toothedgears.

In cases when the externally toothed gear is caused by the wavegenerator to flex in an ellipsoidal shape, the first and second externalteeth formed in the externally toothed gear flex by the same amount inthe radial direction. The first and second external teeth differ interms of module as well as number. The amount by which the firstexternal teeth are flexed to be capable of satisfactorily meshing withinternal teeth of the first internally toothed gear and the amount bywhich the second external teeth are flexed to be capable ofsatisfactorily meshing with internal teeth of the second internallytoothed gear differ from each other.

Therefore, even when the external teeth on one side can satisfactorilymesh with internal teeth, the degree of meshing of the external teeth onthe other side with respect to internal teeth is either insufficient orexcessive. When the degree of meshing of the external teeth with respectto the internal teeth is insufficient, the load capacity of the strainwave gearing and the transmission torque capacity decrease. Conversely,when the degree of meshing of the external teeth with respect to theinternal teeth is excessive, the teeth on both sides interfere with eachother, and the wear resistance thereof decreases. When the meshingstates of the first and second external teeth with respect to theinternal teeth differ, the balance of tooth bottom fatigue strengthbetween the first and second external teeth deteriorates. Furthermore,there will be an increase in the range of fluctuation in thebearing-ball load distribution in first and second wave bearings in thewave generator, the wave bearings supporting the first and secondexternal teeth, and a risk is presented that such increases coulddegrade the service life of the wave bearings.

No dual-type strain wave gearings have been proposed in the prior art.Therefore, no attention has been directed on the states of meshing withinternally toothed gears when left and right first and second externalteeth differing in number are flexed by the same amount, or on theadverse effects caused by such meshing states.

In view of the drawbacks described above, an object of the presentinvention is to provide a dual-type strain wave gearing in which thetooth profiles of first and second external teeth differing in numberare suitably set such that it is possible to flex the first and secondexternal teeth in a suitable manner and form satisfactory meshing stateswith respect to each of the internally toothed gears.

Means of Solving the Problem

In order to solve the problem described above, a dual-type strain wavegearing of the present invention is characterized by including:

a rigid first internally toothed gear in which first internal teeth areformed;

a rigid second internally toothed gear in which second internal teethare formed, the second internally toothed gear being disposed so as tobe coaxially aligned in parallel with the first internally toothed gear;

a flexible externally toothed gear in which first external teeth capableof meshing with the first internal teeth and second external teethcapable of meshing with the second internal teeth are formed in theouter-peripheral surface of a radially flexible cylindrical body, thesecond teeth differing in number from the first teeth, and theexternally toothed gear being disposed coaxially inside the first andsecond internally toothed gears; and

a wave generator which causes the externally toothed gear to flex in anellipsoidal shape, causing the first external teeth to partially meshwith the first internal teeth and causing the second external teeth topartially mesh with the second internal teeth; wherein, a relationshipZf1=Zf2−2nis satisfied, where Zf1 is the number of first external teeth, Zf2 isthe number of second external teeth, and n is a positive integer,

wherein, m₁ is the module of the first external teeth, m₂ is the moduleof the second external teeth,

n₁ and n₂ are positive integers, 2n₁ is the difference in number ofteeth between the first external teeth and the first internal teeth, and2n₂ is the difference in number of teeth between the second externalteeth and the second internal teeth, and

the theoretical value d₁ of the amount by which the first external teethare radially flexed at major-axis positions and the theoretical value d₂of the amount by which the second external teeth are radially flexedwhen the externally toothed gear is flexed in an ellipsoidal shape, arerespectively represented byd₁=m₁n₁ andd₂=m₂n₂;

wherein a radial flexing amount d, which is a radial flexing amount ofthe first and second external teeth being flexed by the wave generator,satisfies relationshipsd<d₁, andd>d₂; and,

wherein, a relationshipα1>α2is satisfied, where a first average pressure angle α1 is the average ofangles that are formed by a tooth-profile center line and atooth-profile tangent line that extends to individual portions of thetooth land within a range of 50% of the total tooth depth in the toothprofile of the first external teeth, the range being centered about thepitch circle of the first external teeth, and

a second average pressure angle α2 is the average of angles that areformed by a tooth-profile center line of the second external teeth and atooth-profile tangent line that extends to individual portions of thetooth land within a range of 50% of the total tooth depth in the toothprofile of the second external teeth, the range being centered about thepitch circle of the second external teeth.

The first and second average pressure angles α1 and α2 preferablysatisfy0.29α1<α2<0.75α1.

In the present invention, the first and second external teeth differingin number are caused to flex in an ellipsoidal shape so as to flex bythe same amount, and are caused to mesh with the first and secondinternal teeth, respectively. With regard to the first external teeth,of which there are a smaller number, the amount of flexing is less thanthe theoretical value. The tooth profile of the first external teeth isconfigured such that the tooth depth and the average pressure anglethereof are greater than those of the tooth profile of the secondexternal teeth. This makes it possible to eliminate any insufficiency inmeshing between the first internal teeth and the first external teeth,which advance less during meshing, and to form a satisfactory meshingstate.

Conversely, with regard to the second external teeth, of which there area greater number, the amount of flexing is greater than the theoreticalvalue. The tooth profile of the second external teeth is configured suchthat the tooth depth and the average pressure angle thereof are lessthan those of the tooth profile of the first external teeth. This makesit possible to eliminate interference between the second internal teethand the second external teeth, which advance more during meshing, and toform a satisfactory meshing state.

As a result, it is possible to eliminate adverse effects such as:degradation of the meshing state between the first external teeth andfirst internal teeth and the meshing state between the second externalteeth and the second internal teeth, which would reduce the loadcapacity of the strain wave gearing; worsening of the balance of toothbottom fatigue strength between the first and second external teeth; anda decrease in wear resistance of the externally toothed gear andinternally toothed gears. Furthermore, in the wave generator forsupporting the first and second external teeth, it is possible tominimize the range of fluctuation in the bearing-ball load distributionin first and second wave bearings, and prevent any reduction in theservice life of the wave bearings.

In the present invention, first and second rim wall thicknesses t(1),t(2) preferably satisfy the relationshipt(1)<t(2),

where the first rim wall thickness t(1) is the rim wall thickness of thetooth bottom rim of the first external teeth, and the second rim wallthickness t(2) is the rim wall thickness of the tooth bottom rim of thesecond external teeth.

Thus, the rim wall thickness of the second external teeth, of whichthere are a greater number, is greater than the rim wall thickness ofthe other first external teeth, of which there are a smaller number.This makes it possible to maintain the balance of tooth bottom fatiguestrength between the first and second external teeth.

Additionally, in the present invention, the wave generator preferablyinclues:

a rigid plug;

an ellipsoidally contoured outer-peripheral surface formed in theouter-peripheral surface of the plug;

a first wave bearing fitted to the outer-peripheral surface, the firstwave bearing comprising ball bearings for supporting the first externalteeth; and

a second wave bearing fitted to the outer-peripheral surface, the secondwave bearing comprising ball bearings for supporting the second externalteeth.

In the dual-type strain wave gearing, the numerical relationship betweeneach of the teeth can be established as described below. Specifically,the number of first external teeth differs from the number of firstinternal teeth, and the number of second external teeth differs from thenumber of second internal teeth.

Specifically, the number of first external teeth is less than the numberof first internal teeth, and the number of first internal teeth and thenumber of second internal teeth are equal to each other.

Furthermore, the dual-type strain wave gearing is typically used as agear reducer. In this case, for example, the wave generator is arotation-inputting element, one of the first internally toothed gear andsecond internally toothed gear is a stationary-side internally toothedgear secured so as not to rotate, and the other of the first internallytoothed gear and second internally toothed gear is a drive-sideinternally toothed gear that is a reduced-rotation-outputting element.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1(A) and FIG. 1(B) are an end-surface view and a longitudinalcross-sectional view of a dual-type strain wave gearing to which thepresent invention is applied;

FIG. 2 is a schematic diagram of the dual-type strain wave gearing shownin FIG. 1(A) and FIG. 1(B);

FIG. 3 is a partial enlarged cross-sectional view of the strain wavegearing shown in FIG. 1(A) and FIG. 1(B);

FIG. 4(A) and FIG. 4(B) are diagrams showing the flexed state of theexternally toothed gear shown in FIG. 1(A) and FIG. 1(B); and

FIG. 5(A) and FIG. 5(B) are pairs of graphs showing the tooth profilesof the first and second external teeth of the externally toothed gearshown in FIG. 1(A) and FIG. 1(B).

MODE FOR CARRYING OUT THE INVENTION

An embodiment of a dual-type strain wave gearing to which the presentinvention is applied is described below with reference to the attacheddrawings.

[Overall Configuration of Strain Wave Gearing]

FIG. 1(A) and FIG. 1(B) are an end-surface view and a longitudinalcross-sectional view showing a dual-type strain wave gearing (referredto below simply as “strain wave gearing”) according to an embodiment ofthe present invention, and FIG. 2 is a schematic diagram of the same.The strain wave gearing 1, which is used as, e.g., a gear reducer, hasan annular rigid first internally toothed gear 2, an annular rigidsecond internally toothed gear 3, a cylindrical flexible externallytoothed gear 4 comprising a radially flexible thin-walled elastic body,and an ellipsoidally contoured wave generator 5.

The first and second internally toothed gears 2, 3 are disposed so as tobe coaxially aligned in parallel with each other, with a prescribed gaptherebetween, along the direction of a central axis 1 a. In the presentexample, the first internally toothed gear 2 is a stationary-sideinternally toothed gear secured so as not to rotate, the number of firstinternal teeth 2 a thereof being indicated by Zc1. The second internallytoothed gear 3 is a rotatably supported drive-side internally toothedgear, the number of second internal teeth 3 a thereof being indicated byZc2. The second internally toothed gear 3 is thereduced-rotation-outputting element of the strain wave gearing 1.

The cylindrical externally toothed gear 4 is disposed coaxially insidethe first and second internally toothed gears 2, 3. The externallytoothed gear 4 has a cylindrical body 6 that is a radially flexiblethin-walled elastic body, first external teeth 7 and second externalteeth 8 formed in the circular outer-peripheral surface of thecylindrical body 6, and a gap 9 (refer to FIG. 3) formed between theexternal teeth 7, 8 on either side, the gap 9 functioning as a cutterclearance area. The first external teeth 7 are formed on one side alongthe central axis 1 a direction of the circular outer-peripheral surfaceof the cylindrical body 6, and the second external teeth 8 are formed onthe other second-internal-teeth 3 a side of the circularouter-peripheral surface. The first and second external teeth 7, 8 areformed such that the central-axis 1 a direction is the tooth tracedirection.

Specifically, the first external teeth 7 are formed on the side opposingthe first internal teeth 2 a, and are capable of meshing with the firstinternal teeth 2 a, the number of first external teeth 7 being indicatedby Zf1. The second external teeth 8 are formed on the side opposing thesecond internal teeth 3 a, and are capable of meshing with the secondinternal teeth 3 a, the number of second external teeth 8 beingindicated by Zf2. The numbers Zf1, Zf2 of teeth are different from eachother.

The wave generator 5 has an ellipsoidally contoured rigid plug 11, and afirst wave bearing 12 and second wave bearing 13, the first and secondwave bearings being fitted to the ellipsoidal outer-peripheral surfaceof the rigid plug 11. The first and second wave bearings 12, 13 areformed from ball bearings.

The wave generator 5 is inserted into the inner-peripheral surface ofthe cylindrical body 6 of the externally toothed gear 4, and causes thecylindrical body 6 to flex in an ellipsoidal shape. Therefore, the firstand second external teeth 7, 8 are also flexed in an ellipsoidal shape.The ellipsoidally flexed externally toothed gear 4 meshes with the firstand second internally toothed gears 2, 3 at both end positions along themajor axis Lmax of the ellipsoidal shape. Specifically, the firstexternal teeth 7 mesh with the first internal teeth 2 a at both endpositions along the major axis of the ellipsoidal shape, and the secondexternal teeth 8 mesh with the second internal teeth 3 a at both endpositions along the major axis.

The wave generator 5 is the rotation-input element of the strain wavegearing 1. The rigid plug 11 of the wave generator 5 has a shaft hole 11c, in which an input rotation shaft 10 (refer to FIG. 2) is securelyconnected in a coaxial arrangement. For example, a motor output shaftmay be securely connected in a coaxial arrangement in the shaft hole 11c. When the wave generator 5 rotates, the positions at which the firstexternal teeth 7 of the externally toothed gear 4 and thestationary-side first internal teeth 2 a mesh, and the positions atwhich the second external teeth of the externally toothed gear 4 and thedrive-side second internal teeth 3 a mesh, move along thecircumferential direction.

The number Zf1 of first external teeth 7 and the number Zf2 of secondexternal teeth 8 differ from each other; in the present example, thenumber Zf2 of second external teeth is greater. The number Zc1 of firstinternal teeth 2 a and the number Zf1 of first external teeth 7 alsodiffer from each other; in the present example, the number Zc1 of firstinternal teeth 2 a is greater. The number Zc2 of second internal teeth 3a and the number Zf2 of second external teeth 8 differ from each other;in the present example, the number Zc2 of second internal teeth 3 a isless.

In the present example, the externally toothed gear 4 is caused to flexin an ellipsoidal shape, and meshes with the internally toothed gears 2,3 at two locations along the circumferential direction. Therefore, thedifference between the number Zc1 of first internal teeth 2 a and thenumber Zf1 of first external teeth 7 is 2n₁, where n₁ is a positiveinteger. The difference between the number Zc2 of second internal teeth3 a and the number Zf2 of second external teeth 8 is 2n₂, where n₂ is apositive integer.Zc1=Zf1+2n ₁Zc2=Zf2−2n ₂

In a specific example, the numbers of teeth are set as follows(n₁=n₂=1):Zc1=62Zf1=60Zc2=62Zf2=64

The speed ratio R1 between the first internally toothed gear 2 and thefirst external teeth 7, and the speed ratio R2 between the secondinternally toothed gear 3 and the second external teeth 8, arerespectively defined as follows:i1=1/R1=(Zf1−Zc1)/Zf1=(60−62)/60=−1/30i2=1/R2=(Zf2−Zc2)/Zf2=(64−62)/64=1/32

Therefore, R1=−30, and R2=32.

The speed ratio R of the strain wave gearing 1 is represented by thefollowing formula using the speed ratios R1, and R2. Thus, according tothe present invention, a strain wave gearing having a dramatically lowspeed ratio (low reduction ratio) can be realized (a negative speedratio indicates that output rotation progresses in the directionopposite that of input rotation).

$\begin{matrix}{R = {( {{R\; 1 \times R\; 2} - {R\; 1}} )/( {{{- R}\; 1} + {R\; 2}} )}} \\{= {( {{{- 30} \times 32} + 30} )/( {30 + 32} )}} \\{= {{- 930}/62}} \\{= {- 15}}\end{matrix}$

Thus, according to the strain wave gearing 1 in the present example, itis possible to obtain a speed ratio of less than 50, e.g., a speed ratioappreciably lower than 30. Additionally, unlike in the prior art, firstexternal teeth 7 and second external teeth 8 that differ in number andmodule are formed as the external teeth of the externally toothed gear.Accordingly, there is a greater degree of freedom in the design forsetting the speed ratio, and a strain wave gearing having a low speedratio can be realized more easily than in the prior art.

[Configuration of Externally Toothed Gear]

FIG. 3 is a partial enlarged cross-sectional view of the strain wavegearing 1 shown in FIG. 1(A) and FIG. 1(B). The first and secondexternal teeth 7, 8 formed in the externally toothed gear 4 shall now bedescribed in detail with reference primarily to FIG. 3. In the presentexample, the tooth width of the first and second external teeth 7, 8 issubstantially equal to that of the first and second internal teeth 2 a,3 a, with which the first and second external teeth 7, 8 are capable ofmeshing. Therefore, the first external teeth 7 and second external teeth8, which have the same tooth width, are formed symmetrically about atooth-trace-direction central position 6 a on the cylindrical body 6. Incases when the first internal teeth 2 a and second internal teeth 3 adiffer in terms of tooth width, the first external teeth 7 and secondexternal teeth 8 are also configured with different tooth widths in acorresponding manner.

The gap 9, which has a prescribed width along the tooth trace direction,is formed between the first and second external teeth 7, 8. The gap 9functions as a cutter clearance area for tooth-cutting cutters used forcutting the first and second external teeth 7, 8.

(Rim Wall Thickness of First and Second External Teeth)

The rim wall thickness of the tooth bottom rim of the first externalteeth 7 and second external teeth 8 is set as follows. The second rimwall thickness t(2) of the second external teeth 8, of which there are agreater number, is set so as to be greater than the first rim wallthickness t(1) of the first external teeth 7, of which there are asmaller number, where the first rim wall thickness t(1) is the rim wallthickness of the first external teeth 7, and the second rim wallthickness t(2) is the rim wall thickness of the second external teeth 8.t(1)<t(2)

(Amount by Which First and Second External Teeth are Flexed)

The first and second external teeth 7, 8 of the externally toothed gear4 in the present example are both caused to flex in an ellipsoidal shapeby the wave generator 5 having the two rows of wave bearings 12, 13. m₁is the module of the first external teeth 7, and m₂ is the module of thesecond external teeth 8. 2n₁ is the difference in number between thefirst external teeth 7 and the first internal teeth 2 a, and 2n₂ is thedifference in number between the second external teeth 8 and the secondinternal teeth 3 a. Therefore, the theoretical value d₁ of the amount bywhich the first external teeth 7 are radially flexed at major-axispositions Lmax and the theoretical value d₂ of the amount by which thesecond external teeth 8 are radially flexed when the external teeth areflexed in an ellipsoidal shape are respectively represented by thefollowing.d₁=m₁n₁d₂=m₂n₂

In the case of the first and second external teeth 7, 8 that differ innumber and are formed in the outer-peripheral surface of the samecylindrical body 6, the pitch circle diameters of the teeth on bothsides are approximately equal. Accordingly, the theoretical value mn ofthe amount of radial flexing is normally less when the number of teethis greater.

In the present example, the amounts by which the first and secondexternal teeth 7, 8 are radially flexed by the wave generator 5 are bothset to amount d. The amount d of radial flexing is represented by thefollowing.d<d₁d>d₂

FIG. 4(A) and FIG. 4(B) are diagrams showing the flexed state of theexternally toothed gear 4. In FIG. 4(A) and FIG. 4(B), the rim-neutralcircle C is the circle passing through the thickness center of thecylindrical body (tooth bottom rim) 6 in a state in which the externallytoothed gear 4 is perfectly circular prior to being flexed in anellipsoidal shape. The rim-neutral circle C is deformed in anellipsoidal shape due to the externally toothed gear 4 being flexed inan ellipsoidal shape. This deformed circle is referred to as the“ellipsoidal rim-neutral curve C1.”

The amount d by which the externally toothed gear 4 is radially flexedis the difference between the radius of the major axis Lmax of theellipsoidal rim-neutral curve C1 and the radius of the rim-neutralcircle C. This amount d is represented by κmn, where m is the module ofthe externally toothed gear, 2n is the difference in number of teethwith respect to the internally toothed gears (n being a positiveinteger), and κ is the deflection coefficient. The amount mn of radialflexing when κ equals 1 is a value obtained by dividing the pitch circlediameter of the externally toothed gear by the reduction ratio from whenthe rigid internally toothed gear is secured; this is the theoreticalvalue (amount of flexing at a standard deflection) of the amount ofradial flexing.

In the present example, the state of flexing of the first external teeth7, of which there are a smaller number, is set to an amount of flexingless than the theoretical value (an amount of flexing at a negativedeflection angle where κ<1), as described above. Conversely, the stateof flexing of the second external teeth 8, of which there are a greaternumber, is set to an amount of flexing greater than the theoreticalvalue (an amount of flexing at a positive deflection angle where κ>1).

(Average Pressure Engles of First and Second External Teeth)

FIG. 5(A) is a graph showing the pressure angle of the tooth profilethat defines the first external teeth 7, and FIG. 5(B) is a graphshowing the pressure angle of the tooth profile that defines the secondexternal teeth 8. The pressure angles of the tooth profiles of the firstand second external teeth 7 and 8 in the present example are describedwith reference to these graphs.

In FIG. 5(A), which shows one tooth profile 70 of the first externalteeth 7, a principal tooth land region A1 is the tooth land region thatdefines a range of 50% of the total tooth depth hl of the tooth profile70, the principal tooth land region A1 being centered about the pitchcircle PC1. The average of the angles that are formed by a tooth-profilecenter line of the tooth profile 70 and a tooth-profile tangent linethat extends to individual portions of the principal tooth land regionA1 is determined, this average being a first average pressure angle α1.

Similarly, in FIG. 5(B), which shows one tooth profile 80 of the secondexternal teeth 8, a principal tooth land region A2 is the tooth landregion that defines a range of 50% of the total tooth depth h2 of thetooth profile 80, the principal tooth land region A2 being centeredabout the pitch circle PC2. The average of angles that are formed by atooth-profile center line of the tooth profile and a tooth-profiletangent line that extends to individual portions of the principal toothland region A2 is determined, this average being a second averagepressure angle α2.

In the present example, the first average pressure angle αl of the firstexternal teeth 7, of which there are a smaller number, is set so as tobe greater than the second average pressure angel α2 of the secondexternal teeth 8, of which there are a greater number (i.e., α1>α2). Forexample, the relationship between the first and second average pressureangles α1, α2 may be established as follows.α2≠0.31α1

According to the experiments carried out by the inventors, it wasconfirmed that the relationship between the first and second averagepressure angles α1, α2 is preferably established as follows.0.29α1<α2<0.75α1

By setting the average pressure angles of the first and second externalteeth 7 and 8 differing in number as described above, the both first andsecond external teeth 7 and 8 can be meshed in a satisfactory mannerwith the corresponding internally toothed gears. In addition, it wasconfirmed that the wear resistance of the first and second externalteeth 7 and 8 is improved, and that the balance of the tooth bottomfatigue strengths between the first and second external teeth 7 and 8 isimproved. It was also confirmed that the bearing-ball load distributionof the two rows of the wave bearings 12 and 13 of the wave generator 5for supporting the first and second external teeth 7 and 8 can be madeuniform, and that the lifetimes of the wave bearings 12 and 13 can beelongated.

(Gap: Cutter Clearance Area)

The gap 9 formed between the first and second external teeth 7, isdescribed next with reference to FIG. 3. As described previously, thegap 9 functions as a cutter clearance area for tooth-cutting cuttersused for cutting the first and second external teeth 7, 8.

The gap 9 has a prescribed width along the tooth trace direction; thedeepest part, which is the part of the gap 9 that is formed deepestalong the tooth depth direction, is formed in the tooth-trace-directioncentral portion. In the present example, the deepest part 9 a is aportion at which the tooth-trace-direction central portion is defined bya straight line extending parallel to the tooth trace direction, asviewed from the tooth-thickness direction. At the twotooth-trace-direction ends of the deepest part 9 a, a concave arcuatecurve that defines the tooth-trace-direction inner-end surface 7 a ofthe first external teeth 7 and a concave arcuate curve that defines thetooth-trace-direction inner-end surface 8 a of the second external teeth8 are smoothly connected. It is also possible to adopt a configurationin which the deepest part 9 a is defined by a concave curved surface andthe two inner-end surfaces 7 a, 8 a are defined by inclined straightlines. It is furthermore possible to adopt a configuration in which thedeepest part 9 a is defined by a straight line and the two inner-endsurfaces 7 a, 8 a are defined by inclined straight lines.

The tooth-trace-direction width of the gap 9 in the present examplegradually increases from the deepest part 9 a along the tooth depthdirection. The maximum width L1 in the tooth trace direction is thedistance, along the tooth trace direction, from thetooth-trace-direction inner end 7 b of the addendum circle of the firstexternal teeth 7 to the tooth-trace-direction inner end 8 b of theaddendum circle of the second external teeth 8.

The relationship0.1L<L1<0.3L

is established, where L is the width from the tooth-trace-directionouter end 7 c of the first external teeth 7 to the tooth-trace-directionouter end 8 c of the second external teeth 8, and L1 is thetooth-trace-direction maximum width of the gap 9.

The depth of the deepest part 9 a of the gap 9 is set as follows. Therelationships0.9h1<t1<1.3h1 and0.9h2<t2<1.3h2

are established, where h1 is the tooth depth of the first external teeth7, h2 is the tooth depth of the second external teeth 8, t1 is thetooth-depth-direction depth from the top land 7 d of the first externalteeth 7 to the deepest part 9 a, and t2 is the tooth-depth-directiondepth from the top land 8 d of the second external teeth 8 to thedeepest part 9 a.

In the externally toothed gear 4 of the dual-type strain wave gearing 1,the tooth-cutting cutters used for cutting the first and second externalteeth 7, 8 are also different from each other. Therefore, the gap 9,which functions as a cutter clearance area, is formed in thetooth-trace-direction central portion of the externally toothed gear 4;i.e., between the first external teeth 7 and the second external teeth8.

The manner in which the gap 9 is formed has a prominent effect on thetooth contact of the first external teeth 7 with respect to the firstinternal teeth 2 a along the tooth trace direction, as well as the toothland load distribution. The manner in which the gap 9 is formedsimilarly has a prominent effect on the tooth contact of the secondexternal teeth 8 with respect to the second internal teeth 3 a along thetooth trace direction, as well as the tooth land load distribution.

In view of these points, the maximum width L1 of the gap is set within arange of 0.1-0.3 times the width L of the externally toothed gear 4, andthe maximum depths t1, t2 are set within a range of 0.9-1.3 times thetooth depths h1, h2 of the first and second external teeth 7, 8, asdescribed above. It was confirmed that forming the gap 9 in this mannermakes it possible to maintain uniformity in the tooth-trace-directiontooth land load distributions of the first and second external teeth 7,8, and to maintain a satisfactory state for the tooth contact of thefirst and second external teeth 7, 8 with respect to the first andsecond internal teeth 2 a, 3 a at each tooth-trace-direction position.

[Distance Between Bearing-Ball Centers in Wave Generator]

The distance between the bearing-ball centers of the first and secondwave bearings 12, 13 are described next with reference to FIG. 3.

In the rigid plug 11 of the wave generator 5, an ellipsoidally contouredfirst outer-peripheral surface 11 a of fixed width is formed on onecentral-axis-direction side, and an ellipsoidally contoured secondouter-peripheral surface 11 b of fixed width is formed on the othercentral-axis-direction side. The first outer-peripheral surface 11 a andthe second outer-peripheral surface 11 b are ellipsoidalouter-peripheral surfaces having the same shape and the same phase.

The first wave bearing 12 is fitted to the first outer-peripheralsurface 11 a in a state of being flexed in an ellipsoidal shape, and thesecond wave bearing 13 is fitted to the second outer-peripheral surface11 b in a state of being flexed in an ellipsoidal shape. The first andsecond wave bearings 12, 13 are of the same size.

The bearing centers 12 a, 13 a of the first wave bearing 12 and secondwave bearing 13 are located at positions that are equidistant, along thetooth width direction, from the tooth-trace-direction central position 6a on the externally toothed gear 4. The distance between bearing-ballcenters is set so as to increase correspondingly with an increase in themaximum width L1 of the gap 9. Furthermore, the inter-ball-centerdistance Lo is set so as to reach a value within the range indicated bythe following formula, Lo being the distance between bearing-ballcenters.0.35L<Lo<0.7L

In the prior art, a wave generator having two rows of ball bearings isused in order to increase the area in which the externally toothed gearis supported. The two rows of ball bearings were arranged with respectto the tooth-width-direction central portion of the externally toothedgear, irrespective of the inter-ball-center distance.

In the present example, the inter-ball-center distance Lo between tworows of wave bearings 12, 13 is increased such that it is possible toincrease rigidity for supporting first and second external teeth 7, 8differing in number, and to improve the tooth contact of each of theexternal teeth 7, 8 with respect to internal teeth 2 a, 3 a at eachtooth-trace-direction position. Specifically, as described above, aconfiguration is adopted in which the inter-ball-center distance Lolengthens (increases) correspondingly with an increase in thetooth-trace-direction maximum length L1 of the gap 9, which is formedbetween the first and second external teeth 7, 8 and functions as acutter clearance area. The range of increase of the inter-ball-centerdistance Lo is set to 0.35-0.7 times the width L of the externallytoothed gear 4.

This makes it possible to arrange the first and second wave bearings 12,13 such that the ball centers are positioned at suitabletooth-trace-direction positions with respect to each of the first andsecond external teeth 7, 8, in accordance with the width of the gap 9that is formed. This makes it possible to reliably support the first andsecond external teeth 7, 8, using the first and second wave bearings 12,13, at each tooth-trace-direction position of each of the first andsecond external teeth 7, 8 (i.e., to increase the supporting rigidity ofthe wave generator 5).

As a result, it is possible to improve the tooth contact of the firstand second external teeth 7, 8 at each tooth-trace-direction position,and to increase the tooth bottom fatigue strength thereof. It is alsopossible to average the bearing-ball load distribution of each of thewave bearings 12, 13 of the wave generator 5, and to reduce the maximumload; therefore, the service life of the wave generator 5 can beimproved.

Other Embodiments

In the example described above, the first internally toothed gear 2 isconfigured as a stationary-side internally toothed gear, and the secondinternally toothed gear 3 is configured as a drive-side internallytoothed gear (reduced-rotation-outputting member). However, it ispossible to instead configure the first internally toothed gear 2 as adrive-side internally toothed gear (reduced-rotation-outputting member),and configure the second internally toothed gear 3 as a stationary-sideinternally toothed gear.

The invention claimed is:
 1. A strain wave gearing comprising: a rigidfirst internally toothed gear formed with first internal teeth; a rigidsecond internally toothed gear formed with second internal teeth, thesecond internally toothed gear being disposed so as to be coaxiallyaligned in parallel with the first internally toothed gear; a flexibleexternally toothed gear in which first external teeth capable of meshingwith the first internal teeth and second external teeth capable ofmeshing with the second internal teeth are formed in an outer-peripheralsurface of a radially flexible cylindrical body, the second teethdiffering in number from the first teeth, and the externally toothedgear being disposed coaxially inside the first and second internallytoothed gears; and a wave generator for flexing the externally toothedgear in an ellipsoidal shape to cause the first external teeth topartially mesh with the first internal teeth and to cause the secondexternal teeth to partially mesh with the second internal teeth,wherein, a relationshipZf1=Zf2−2n is satisfied, where Zf1 is the number of first externalteeth, Zf2 is the number of second external teeth, and n is a positiveinteger; wherein, a radial flexing amount d, which is a radial flexingamount of the first and second external teeth being flexed by the wavegenerator, satisfiesd<d₁, andd>d₂, where m₁ is a module of the first external teeth, m₂ is a moduleof the second external teeth, n₁ and n₂ are positive integers, 2n₁ is adifference in number of teeth between the first external teeth and thefirst internal teeth, and 2n₂ is a difference in number of teeth betweenthe second external teeth and the second internal teeth, and atheoretical value d₁ of an amount by which the first external teeth areradially flexed at major-axis positions and a theoretical value d₂ of anamount by which the second external teeth are radially flexed when theexternally teethed gear is flexed in an ellipsoidal shape arerespectively represented byd₁=m₁n₁ andd₂=m₂n₂; and wherein, a relationshipα1>α2 is satisfied, where a first average pressure angle α1 is anaverage of angles that are formed by a tooth-profile center line and atooth-profile tangent line that extends to individual portions of atooth land within a range of 50% of a total tooth depth in a toothprofile of the first external teeth, the range being centered about apitch circle of the first external teeth, and where a second averagepressure angle α2 is an average of angles that are formed by atooth-profile center line of the second external teeth and atooth-profile tangent line that extends to individual portions of atooth land within a range of 50% of a total tooth depth in a toothprofile of the second external teeth, the range being centered about apitch circle of the second external teeth.
 2. The strain wave gearingaccording to claim 1, wherein the first and second average pressureangles α1 and α2 satisfy0.29α1<α2<0.75α1.
 3. The strain wave gearing according to claim 1wherein first and second rim wall thicknesses t(1) and t(2) satisfyt(1)<t(2), where the first rim wall thickness t(1) is a rim wallthickness of a tooth bottom rim of the first external teeth, and thesecond rim wall thickness t(2) is a rim wall thickness of a tooth bottomrim of the second external teeth.
 4. The strain wave gearing accordingto claim 1, wherein the wave generator has: a rigid plug; anellipsoidally contoured outer-peripheral surface formed in anouter-peripheral surface of the plug; a first wave bearing fitted to theouter-peripheral surface, the first wave bearing comprising ballbearings for supporting the first external teeth; and a second wavebearing fitted to the outer-peripheral surface, the second wave bearingcomprising ball bearings for supporting the second external teeth. 5.The strain wave gearing according to claim 1, wherein a gap is formedbetween a tooth-trace-direction inner-end surface of the first externalteeth and a tooth-trace-direction inner-end surface of the secondexternal teeth, the gap having a prescribed width along a tooth tracedirection, and the gap having a deepest part along a tooth depthdirection at a tooth-trace-direction central portion; wherein arelationship0.1L<L1<0.3L is satisfied, where L is a width from atooth-trace-direction outer end of the first external teeth to atooth-trace-direction outer end of the second external teeth, and L1 isa maximum width of the gap along the tooth trace direction; and, whereinrelationships0.9h1<t1<1.3h1 and0.9h2<t2<1.3h2 are satisfied, where h1 is a tooth depth of the firstexternal teeth, h2 is a tooth depth of the second external teeth, t1 isa tooth-depth-direction depth from a tooth top land of the firstexternal teeth to the deepest part, and t2 is a tooth-depth-directiondepth from a tooth top land of the second external teeth to the deepestpart.
 6. The strain wave gearing according to claim 5, wherein the wavegenerator has a first wave bearing comprising a ball bearing forsupporting the first external teeth, and a second wave bearingcomprising a ball bearing for supporting the second external teeth;wherein bearing-ball centers of the first wave bearing and the secondwave bearing are located at positions that are equidistant, along thetooth trace direction, from a tooth-trace-direction center of the gap;and wherein, where an inter-ball-center distance Lo is a distancebetween the bearing-ball centers of the first and second wave bearings,the inter-ball-distance is set so as to increase correspondingly with anincrease in the maximum width L1 of the gap, and satisfies arelationship0. 35L<Lo<0.7L.
 7. The strain wave gearing according to claim 1, whereinthe number of the first external teeth differs from the number of thefirst internal teeth, and the number of second external teeth differsfrom the number of second internal teeth.
 8. The strain wave gearingaccording to claim 1, wherein the number of first external teeth is lessthan the number of first internal teeth, and the number of firstinternal teeth and the number of second internal teeth are equal to eachother.
 9. The strain wave gearing according to claim 1, wherein the wavegenerator is a rotation-inputting element; and either one of the firstinternally toothed gear and second internally toothed gear is astationary-side internally toothed gear secured so as not to rotate, andthe other of the first internally toothed gear and second internallytoothed gear is a drive-side internally toothed gear that is areduced-rotation-outputting element.